Home> TE mode in circular wave-guide

parameters	express
Azimuth mode number	\( \)
Radial mode number	\( \)
Radius of the wave guide	\( mm\)
Frequency	\( GHz\)
Analysis total modes m	\( \)
Analysis total modes n	\( \)
\(\chi_{mn}'\)	\(J'_m(\chi)=0\)
cutoff wave number	\(k_c=\chi_{mn}/a\)
cutoff frequency	\(k_c=k=\frac{\omega}{c}=\frac{2 \pi f_c}{c}\)
cutoff wave length	\(c=\lambda_c k_c\)
wave number for f0	\(k=\frac{\omega}{c}=\frac{2 \pi f_0}{c}\)
axial wave number	\(k^2=k_c^2+k_z^2\)
waveguide wavelength	\(\lambda_g k_z=2\pi\)
electron beam radius	\(max J_{m-1}'(k_c r_b)\)

\(k_z=const \,\,\,and \,\,k=\frac{2\pi f}{c}=\sqrt{k_z^2+\frac{\chi_{mn}}{a}^2}\Rightarrow \Delta f=f-f_0\)